Liquid crystal display system with internally reflecting waveguide for backlighting and non-Lambertian diffusing

ABSTRACT

Systems and methods for providing an LCD with a collimated backlight and a non-Lambertian diffuser are described. An LCD system includes: an illumination source for producing light; a collimating waveguide optically connected to the illumination source, the collimating waveguide including a top surface, an incident end and a plurality of substantially parallel optical elements for redirecting light from the incident end to, and through, the top surface, each of the plurality of substantially parallel optical elements including a first facet that is nonparallel to the top surface and a second facet that is nonparallel to the top surface; a reflector optically connected to the light source and optically connected to the collimating waveguide, the reflector (1) at least partially surrounding the illumination source, and (2) reflecting light from said illumination source to said incident end by direct reflection; a liquid crystal display optically connected to the collimating waveguide; and a non-Lambertian diffuser optically connected to the liquid crystal display for directing light from said liquid crystal display. The light from the reflector is directly incident upon the incident end. The systems and methods provide advantages in that the light from the LCD is bright and homogenous.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates in general to the field of liquid crystaldisplay (LCD) systems. More particularly, the present invention relatesto a liquid crystal display that is illuminated with collimatedbacklighting. In a preferred embodiment, the present invention relatesto a liquid crystal display system that includes a collimating backlightand a non-Lambertian diffuser. The present invention thus relates toliquid crystal display systems of the type that can be termed collimatedbacklit non-Lambertian diffused.

2. Discussion of the Related Art

Within this application, several publications are referenced by arabicnumerals within parentheses. Full citations for these, and other,publications may be found at the end of the specification immediatelypreceding the claims. The disclosures of all these publications in theirentireties are hereby expressly incorporated by reference into thepresent application for the purposes of indicating the background of thepresent invention and illustrating the state of the art.

Historically, it has been known in the prior art to illuminate liquidcrystal displays. Liquid crystal displays of the type hereunderconsideration are well-known to those skilled in the art. A conventionalliquid crystal display is typically illuminated with a backlight device.Such a backlight device typically includes an illumination sourcelocated at one edge of a planar waveguide. For example, prior art liquidcrystal display backlights have been based on a rectilinear waveguidehaving a transparent top surface and a metallized bottom surface. Suchbacklights are conventionally powered by a single fluorescent lamplocated at one edge of the rectilinear waveguide, or by two lampslocated at two edges.

As is known to those skilled in the art, the light from such anillumination source must be coupled into the waveguide in order toilluminate the liquid crystal display. In the past, this coupling hasbeen inefficient. Thus, a previously recognized problem has been thatmuch of the light available from the illumination source is wastedresulting in decreased brightness. Needless to say, it is desirable toprovide a backlit liquid crystal display having higher brightness.

What is needed therefore is an apparatus that efficiently couples lightfrom the illumination source into the waveguide. However, efficientcoupling between the illumination source and the waveguide is notsufficient. Liquid crystal displays require collimated incident lightand include a polarizer. Therefore, what is also needed is an apparatusthat collimates and redirects the light from the illumination source sothat the maximum amount of light from the illumination source can becoupled through the polarizer of the liquid crystal display. Collimationinvolves minimizing divergence. What is also needed is an apparatus thatnot only increases the brightness, but also provides anamorphic, (i.e.,non-Lambertian), illumination, (e.g., different divergences in thehorizontal and vertical directions).

Another previously recognized problem has been that liquid crystaldisplays are not bright enough for use in high ambient light conditions.Therefore, what is also needed is an apparatus that increases thebrightness of a liquid crystal display. By increasing the overallcoupling efficiency, a liquid crystal display will appear brighter.Alternatively, a lower power illumination source can be used to achievethe same brightness. Needless to say, it is desirable to provide abacklit liquid crystal display having lower power consumption.

Another previously recognized problem has been that the lighttransmitted through liquid crystal display systems is not homogeneous.Typically, the area of the liquid crystal display that is closest to theillumination source, or illumination spots, will be brighter. Therefore,what is also needed is a backlit liquid crystal display with morehomogenous light distribution.

One unsatisfactory previously recognized approach, which attempts tosolve the efficiency and homogeneity problems referred to herein,involves replacing the metallized bottom surface with a surface thatincludes a number of white dots. The density of the dots is proportionalto the distance to the illumination source so that the backlightilluminates a liquid crystal display with greater homogeneity. However,this previously recognized approach has the disadvantage of relativelylow coupling efficiency. Further, this previously recognized approachalso has the disadvantage that the white dots do not collimate thelight.

Moreover, this previously recognized approach also has the disadvantageof relatively high cost. The manufacture and sale of LCD systems is acompetitive business. A preferred solution will be seen by the end-useras being cost effective. Therefore, what is also needed is a liquidcrystal display system that is cost effective. A solution is costeffective when it is seen by the end-user as compelling when comparedwith other potential uses that the end-user could make of limitedresources.

Yet another previously recognized problem has been that much of thelight transmitted through liquid crystal display systems is wastedbecause it is not seen. The eyes of a viewer occupy a relativelylocalized position with respect to the liquid crystal display. Theliquid crystal display will appear brighter if the light that isavailable from the liquid crystal display is directed to the viewer'seye. Therefore, what is also need is a backlit liquid crystal displayhaving directionality. Heretofore the above-discussed requirements havenot been fully met.

The below-referenced U.S. patents, and allowed U.S. application in whichthe issue fee will be paid, disclose embodiments that were at leastin-part satisfactory for the purposes for which they were intended. Thedisclosures of all the below-referenced prior U.S. patents andapplication, in their entireties, are hereby expressly incorporated byreference into the present application for purposes including, but notlimited to, indicating the background of the present invention andillustrating the state of the art.

U.S. Pat. No. 5,390,276 discloses a backlight assembly utilizingmicroprisms. U.S. Pat. No. 5,365,354 discloses a GRIN type diffuserbased on volume holographic material. U.S. Pat. No. 5,359,691 disclosesa backlighting system with a multi-reflection light injection system.U.S. Pat. No. 5,253,151 discloses luminaire for use in backlighting aliquid crystal display matrix. U.S. Pat. No. 5,050,946 discloses afaceted light pipe. U.S. Pat. No. 5,202,950 discloses a backlightingsystem with faceted light pipes. U.S. Ser. No. 08/393,050 discloses alight source destructuring and shaping device.

SUMMARY AND OBJECTS OF THE INVENTION

By way of summary, the present invention is directed to a liquid crystaldisplay system having a collimating backlight and a non-Lambertiandiffuser. An effect of the present invention is to project light througha liquid crystal display.

A primary object of the invention is to provide an apparatus thatefficiently couples light from the illumination source into thewaveguide. Another object of the invention is to provide an apparatusthat collimates the light from the illumination source so that themaximum amount of light from the illumination source can be coupledthrough the polarizer of the liquid crystal display. Another object ofthe invention is to provide an apparatus that increases the brightnessof a liquid crystal display. Another object of the invention is toprovide an apparatus having lower power consumption. Another object ofthe invention is to provide an apparatus with more homogenous lightdistribution. Another object of the invention is to provide an apparatusthat is cost effective. Another object of the invention is to provide anapparatus having directionality. Another object of the invention is toprovide an apparatus that is rugged and reliable, thereby decreasingdown time and operating costs. Another object of the invention is toprovide an apparatus that has one or more of the characteristicsdiscussed above but which is relatively simple to manufacture andassemble using a minimum of equipment.

In accordance with a first aspect of the invention, these objects areachieved by providing an apparatus comprising an illumination source forproducing light; a first distributed wedge collimating waveguideoptically connected to said illumination source, said first distributedwedge collimating waveguide including a top surface, an incident end anda first plurality of substantially parallel optical elements forredirecting light from said incident end to said top surface and throughsaid top surface by leakage, each of said first plurality ofsubstantially parallel optical elements including a first facet that isnonparallel to said top surface and a second facet that is nonparallelto said top surface; a second distributed wedge collimating waveguideoptically connected to said first distributed wedge collimatingwaveguide, said second distributed wedge collimating waveguide includingan upper surface and a second plurality of substantially paralleloptical elements for redirecting light that is leaked through said topsurface through said upper surface; and a reflector optically connectedto said light source and optically connected to said first distributedwedge collimating waveguide, said reflector (1) at least partiallysurrounding said illumination source, and (2) reflecting light from saidillumination source to said incident end by direct reflection. In oneembodiment, a liquid crystal display is optically connected to saidupper surface and a non-Lambertian diffuser is optically connected tosaid liquid crystal display for directing light from said liquid crystaldisplay.

Another object of the invention is to provide a method that can be usedto illuminate a liquid crystal display. Another object of the inventionis to provide a method that is predictable and reproducible, therebydecreasing variance and operating costs. Another object of the inventionis to provide a method that has one or more of the characteristicsdiscussed above but which is which is relatively simple to setup andoperate using relatively low skilled workers.

In accordance with a second aspect of the invention, these objects areachieved by providing a method of illuminating a liquid crystal displaywhich utilizes an apparatus comprising: an illumination source; a firstcollimating waveguide optically connected to said illumination source,said first collimating waveguide including a top surface, an incidentend and a first plurality of substantially parallel optical elements forredirecting light from said incident end to, and through, said topsurface each of said first plurality of substantially parallel opticalelements including a first facet that is nonparallel to said top surfaceand a second facet that is nonparallel to said top surface; a secondcollimating waveguide optically connected to said first collimatingwaveguide, said second collimating waveguide including an upper surfaceand a second plurality of substantially parallel optical elements forredirecting light from said top surface through said upper surface; anda reflector optically connected to said light source and opticallyconnected to said first distributed wedge collimating waveguide, whereineach of said second plurality of substantially parallel optical elementsis an imaging optic. In one embodiment, the second facet of each of saidfirst plurality of substantially parallel optical elements is concavewith respect to said top surface.

These, and other, aspects and objects of the present invention will bebetter appreciated and understood when considered in conjunction withthe following description and the accompanying drawings. It should beunderstood, however, that the following description, while indicatingpreferred embodiments of the present invention, is given by way ofillustration and not of limitation. Many changes and modifications maybe made within the scope of the present invention without departing fromthe spirit thereof, and the invention includes all such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

A clear conception of the advantages and features constituting thepresent invention, and of the construction and operation of typicalmechanisms provided with the present invention, will become more readilyapparent by referring to the exemplary, and therefore nonlimiting,embodiments illustrated in the drawings accompanying and forming a partof this specification, wherein like reference numerals designate thesame elements in the several views, and in which:

FIG. 1 illustrates a perspective view of a conventional liquid crystaldisplay backlight, appropriately labeled "PRIOR ART"; and

FIG. 2 illustrates a partial sectional view of a portion of theconventional liquid crystal display backlight shown in FIG. 1,appropriately labeled "PRIOR ART";

FIG. 3 illustrates a schematic view of a liquid crystal display systemaccording to the present invention;

FIG. 4 illustrates a perspective view of a liquid crystal displaybacklight according to the present invention;

FIG. 5 illustrates a partial sectional view of the liquid crystaldisplay backlight shown in FIG. 4;

FIG. 6 illustrates a partial sectional view of another liquid crystaldisplay backlight according to the present invention;

FIG. 7 illustrates a partial sectional view of a collimating waveguideaccording to the present invention;

FIG. 8 illustrates a perspective view of a collimating waveguideaccording to the present invention;

FIG. 9 illustrates a sectional view of a wedge collimating waveguideaccording to the present invention;

FIG. 10 illustrates a sectional view of a distributed wedge collimatingwaveguide according to the present invention;

FIG. 11 illustrates an elevational view of a portion of a liquid crystaldisplay system according to the present invention;

FIG. 12 illustrates a partial sectional view of a portion of the liquidcrystal display system shown in FIG. 11;

FIG. 13 illustrates a partial sectional view of a collimating waveguideaccording to the present invention;

FIG. 14 illustrates a partial sectional view of a liquid crystal displaysystem according to the present invention;

FIG. 15 illustrates a partial sectional view of a collimating waveguideaccording to the present invention;

FIG. 16 illustrates a schematic sectional view of a portion of thecollimating waveguide shown in FIG. 15;

FIG. 17A illustrates a perspective view of a portion of a collimatingwaveguide according to the present invention;

FIG. 17B illustrates a perspective view of a portion of an imagingcollimating waveguide according to the present invention;

FIG. 17C illustrates a perspective view of a portion of a collimatingwaveguide according to the present invention;

FIG. 18 illustrates a schematic view of a recording configuration formaking diffusers according to the present invention;

FIG. 19 illustrates a partial sectional view of a collimating waveguideaccording to the present invention;

FIG. 20 illustrates a geometrical construction of a portion of acollimating waveguide according to the present invention;

FIG. 21 illustrates a geometrical construction of a portion of acollimating waveguide according to the present invention;

FIG. 22 illustrates a geometrical construction of a portion of acollimating waveguide according to the present invention;

FIG. 23 illustrates a portion of a collimating waveguide according tothe present invention;

FIG. 24 illustrates a portion of a collimating waveguide according tothe present invention;

FIG. 25 illustrates a portion of a collimating waveguide according tothe present invention; and

FIG. 26 illustrates a portion of a collimating waveguide according tothe present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention and the various features and advantageous detailsthereof are explained more fully with reference to the nonlimitingembodiments described in detail in the following description. Beforedescribing the present invention in detail, a graphical review of priorart structures in FIGS. 1-2 is in order.

Referring to FIG. 1, a conventional liquid crystal display backlight isshown where light from illumination source 1 travels to backlightinglight pipe 2 through separate light pipe 3. Separate light pipe 3 isdivided into a number of laterally adjacent sections.

Referring now to FIG. 2, a partial cross sectional view of thebacklighting light pipe 2 in FIG. 1 is shown. The divergence of theincoming light is reduced.

1. SYSTEM OVERVIEW

The above-mentioned requirements of high brightness, low powerconsumption, homogeneity and directionality are to some extent mutuallycontradicting and cannot be satisfied simultaneously in the case of aconventional liquid crystal display system. However, it is renderedpossible to simultaneously satisfy these requirements to a certainextent by employing a collimating waveguide together with anon-Lambertian diffuser in consideration of the fact that thecollimating waveguide tailors the light for use in the liquid crystaldisplay while the non-Lambertian diffuser tailors and homogenizes thelight for viewing by an observer.

Referring to the drawings, it can be seen that the present inventionincludes a generally planar collimating waveguide assembly provided withfacets. For example, FIG. 4 shows an isometric view of a light engine 90connected to a waveguide collimator assembly 1000. Pursuant to thepresent invention, the collimating waveguide assembly can be embodied inseveral nonmutually exclusive configurations. Subcomponents of theseconfigurations are interchangeable and can be combined.

Referring to FIG. 3, light engine 10 is connected to waveguidecollimator 25. Waveguide collimator 25 is connected to homogenizingdiffuser 30. Liquid crystal display 40 is connected to diffuser 30.Light shaping diffuser 45 is connected to liquid crystal display 40. Anadditional light engine 50 can also be connected to waveguide collimator25. The order of light shaping diff-user 30 and liquid crystal display40 can be reversed.

2. GENERAL DESCRIPTION

The liquid crystal display system includes several components. Thesecomponents can include an illumination source, a reflector, one or morenonimaging optics, a collimating waveguide assembly, adiffuser/homogenizer, a liquid crystal display and a non-Lambertiandiffuser.

Illumination Sources

According to Liouvilles' theorem, for an optimized light engine, theinput distribution is almost uniform; therefore, Lambertian. Thefollowing Equation (42) is a result of Liouvilles' theorem. As discussedby Welford and Winston.sup.(1) and by Winston and Jannson.sup.(2) D isthe width of the waveguide. d is the diameter of the emitter, or source.β is the output angle in air:

    d sin 90°=D sin β                              (42)

The 90° factor in Equation (42) is based on the fact that light iscoming from the source in all directions. The optimum light collimatingengine, according to Equation (42), provides not only maximumcollimation (i.e., minimum angle β), but also uniform illumination.Those related designs that are almost optimum are also applicable tothis invention.

Reflectors

The reflector is preferably an extended source arcuate mirror. The termarcuate describes an arc, or curve in 2, or 3, dimensions.Welford.sup.(1) has discussed optimum collimation of light emitted by anextended source, especially spherical and cylindrical sources. Theoptimum design of the reflector is very characteristic of the intendedlight source and is not actually parabolic. A parabolic shape isactually unsatisfactory for extended sources. An arcuate mirrorstructure can provide an ideal fixture for attachment of the lightsource to the rest of the structure. As the illumination source movesaway from the transformer, optimization of the design of the extendedsource arcuate mirror reflector increases in importance.

Collimating Waveguides

In order to be collimated, light must first be coupled into thecollimating waveguide. Coupler configurations such as shown in FIG. 7are well known in the art for use in communications applications. But inthe typical communication application, the waveguide, (e.g., opticalfiber), has a width of approximately 100 microns, or less. In thepresent application the width approaches several millimeters.

FIG. 7 represents a theoretical construction of a waveguide into whichlight is being coupled. Light which is incident normal to the entry edgeof the waveguide passes directly into it without being refracted. Lightat an angle is refracted. According to Snell's law, low light enteringnon-normal to the incident surface is collimated. The first casescenario light at 90° is coupled at a critical angle of approximately40° given an index of refraction for the media of 1.55. The incidentangle in the waveguide α is equal to approximately 50°. This value isapproximately 50° and larger than α_(c) so all of the light which entersthe waveguide collimator is contained within the waveguide collimator bytotal internal reflection (TIR). FIG. 7 illustrates that light enteringthe waveguide will remain trapped within the waveguide due to totalinternal reflection (TIR). Even for the worst case of 90°, incidentangle, the light will still become trapped within the waveguide. Thelight enters the waveguide under α_(c), the critical angle, when##EQU1## assuming that the medium outside the waveguide is air and thewaveguide is constructed of a transparent material having an index ofrefraction n. Typical low cost materials from which the waveguide can befabricated are plastics, adhesives and glass. For these materials, thetypical refractive index is approximately 1.55. Therefore, the criticalangle, α_(c), is approximately 40°. Within the waveguide due totrigonometrical relationships a must be equal to approximately 50°.Therefore, all light is trapped within the waveguide because α isgreater than α_(c). For α larger than α_(c), total internal reflection(TIR) will occur. Total internal reflection (TIR) means that thereflection is exactly 100%. If α is smaller than α. light will be leakedoutside the waveguide (leakage not shown). And the leak can besignificant, more than 50%. Therefore, there is an abrupt transitionwhen the angle moves from less than α_(c) to greater than α_(c). Due tothe fact that even for 90° you have an α_(c) for the transition from airto a material of index 1.55, collimation of the light from theillumination source is provided amounting to a change from an angularrange of from 0° to 90° to an angular range of from 0° to approximately40°. Even without any structural collimating system collimation beforeentry into the waveguide can occur only when d, diameter of source, isless than D, width of the waveguide. For practical reasons, D should beminimized. Thus, the usefulness of the initial air-material interfacecollimation is limited by the fact that collimation occurs at theinterface. The apparatus disclosed in U.S. Pat. Nos. 5,390,276 and5,359,691 realize only one collimation factor, this being collimationfrom the source via a parabolic reflector, which as discussed above isnot of optimum shape for an extended source as broadly discussed inWelford.sub.(1). The figures in these patents indicate that the spacewithin the reflector is filled with solid material which zeros theair-material interface collimation factor discussed above. Collimationas discussed in U.S. Pat. Nos. 5,359,691 and 5,390,276 is not actuallycollimation because of the fact that the triangular prisms which areprovided only on the bottom of the backlighting light pipe result in aharvesting of only half of the available light. Moreover, extending therays out of the media and into the air would result in de-collimationdue to Snell's law. This results in de-collimation of 56° correspondingto a half angle of 15.6° versus a half angle of 10°, assuming the indexof refraction of the media is 1.55, as before.

Collimating waveguides can be based on either metallic reflection ortotal internal reflection (TIR). In the first case the waveguide isempty, usually. In the second case the waveguide is material filled.Generally, the second, total internal reflection (TIR) case is betterbecause total internal reflection (TIR) gives exactly 100% reflectionwhile metallic reflection can easily drop to 80% due to surface dirt,contamination. Prior art waveguides for this application generally haveone metallized side, for backlighting applications, (e.g., U.S. Pat. No.5,381,309, the entire contents of which are hereby expresslyincorporated by reference). A transformer is a generalized waveguidestructure that not only transmits light through the waveguide but canalso change the direction of this light. A transformer that changes thedirection of light by 90° (orthogonally) can be used to deliberatelyleak light in a preferred direction for use in an application. Prior artpatents show several different ways of designing these leaks. Forexample, U.S. Pat. No. 5,390,276 discloses the use of a retroreflectingscreen polarizer for further collimating the light in order toilluminate an LCD.

A major object of the invention is to provide maximum uniformbacklighting for an LCD, and at the same time provide light that ishighly collimated. A diffuser homogenizes light, but in order for thediffuser to operate properly with an LCD, the light reaching thediffuser must be collimated. Collimation begins when the light engineincident rays enter the waveguide. Secondary collimation can occur whenthe light is taken from the horizontal direction and deflected towardthe vertical direction within the waveguide.

This first description concerns collimation which occurs as the lightenters the waveguide from the source. One hundred percent collimatingefficiency cannot be achieved if the diameter of the source is largerthan the diameter of the waveguide. On the other hand, if the diameterof the source is equal to or less than the diameter of the waveguideoptimum efficiency can be approached. As a practical matter, losses fromthe mirrors prohibit 100% coupling. Any discussion of 100% couplingtherefore implies that the absorptive losses due to interaction of thelight with the mirror is being neglected. Design of the reflector mustbe optimized for a particular d/D ratio. Welford.sup.(1) provides idealdesigns for any possible ratio. The ideal design means that theLiouville theorem is satisfied. Satisfaction results in 100% beingcoupled to the waveguide. The ideal design also means that thedistribution of light within the waveguide will be homogenous. Any ofthe resulting designs will be quite far from being parabolic. Aparabolic design is only optimum for a point, or line, source. Thevolume defined by the interior of the reflector can be filled with amedia or be simply air. In either case the interior surface of thereflector must be mirrorized (e.g., metallized). Although the reflectionefficiency for deep IR and near IR can approach unity, the reflectionefficiency for energy within the visible spectra can easily drop tobetween 90 and 80% due to inefficiency such as dirt on the surface.Maximum reflection efficiency for any wavelength is approximately 96%assuming a metallized mirror surface. In contrast, total internalreflection (TIR) is always 100%. The metallic is never 100% even in theIR case. Preferably the interior of the reflector should be simply airin order to maximize a collimating effect of Snell's law. Even if thediameter of the source is larger than the thickness of the waveguide theworst case 90° incidence light will be collimated to approximately 40°.Deflection design can still be optimized although it will be impossibleto reach 100% coupling. Designs for the large laminar situation will besimilar to what is shown in FIG. 5 and even further from parabolic.

A discussion of the distribution of scattering centers follows.Referring to FIG. 8, the grooves will have variable spacing, Δx. Itshould be noted that the microgrooves do not need to be continuous. Notethat the scattering centers can be separated which is illustrated by thebroken lines. I_(o) represents incident light coming from the left. I isthe intensity after passing through scaler distance x. Total length ofthe device is L. dx represents an infinitesimally small portion of thescaler distance x. FIG. 8 shows a section with dx illustrated. In thegeneral geometry, I is input intensity from the left, reduced to I-dIbecause dI is leaked to the bottom. This property holds for anycoordinate x. General Equation (1) indicates that the lost leakage oflight -dI must be proportional to I.

    -dI=aIρdx                                              (1)

dI is also proportional to the thickness dX, as well as to the densityof grooves which is represented by ρ. a is a proportionality constantwhich will be interpreted below. Equation (2) indicates that the densityis equal to the number of grooves per unit incremental distance.##EQU2## So the units for ρ are cm⁻¹. I=I_(o), for x=0. The number ofgrooves per infinitesimal length dx is dN. N_(t) is the total number ofgrooves. In order to preserve uniform leakage, dI must be proportionalonly to dx. As I necessarily decreases as one moves across the device, ρmust correspondingly increase. Equation (4) is the same as Equation (1)but substituting A for Iρ, for uniform leakage condition:

    dI=-aAdx                                                   (4)

Since a and A are both constant integration yields Equation (5).

    I=I.sub.o -aAx                                             (5)

Equation (6) represents that the density of grooves is equal to aconstant divided by Equation (5), following directly: ##EQU3##Therefore, ρ is a function of x and increases monotonically from P_(o).A discussion of the physical meaning of A and a follows. Both areconstants. ##EQU4## Interpreting Equation (6B) yields Equation (6C).

    I=I.sub.I.sub.o e.sup.-aN                                  (6C)

Equation (7) defines a. ##EQU5## dI/I represents the relative leakage.dN is the number of grooves per infinitesimal length. a is percentage ofleakage per groove. Equation (8) represents that intensity at the fulllength L is O. ##EQU6## Equation (8) represents a singularity becausethe density of ρ at the full length L cannot reach infinity. Forpractical purposes, it can be assumed that no more than 5% of theavailable light is linked all the way to the end. In addition, a mirrorcan be placed at the end to reflect the light back toward the source.Equation (18) represents aN=3 with the exponent given a value of -3.This, according to Equation (6C), corresponds to 5% of the light beingleft at the reflective end in the waveguide. This light would bereflected back.

    aN=3 I=I.sub.o e.sup.-3 ≈0.05 I.sub.o              (18)

Having a higher density would result in less light left at the end ofthe length, but that could be limited by the physical possibility ofcompacting the grooves. Equation (20) represents the total number ofgrooves, equal to the length divided by Δx which is the average distancebetween grooves, Δx: ##EQU7## The following example uses an averagelength between grooves of 100 microns across a total length slab of 20cm yielding a total number of grooves of approximately 2000 asrepresented in Equation (21). ##EQU8## Equation (19) can now becalculated because N_(T) is known.

    aN.sub.T =3                                                (19)

Equation (22) represents that a is equal to ##EQU9## The average leakageper groove is thus 1.5×10⁻³ as represented in Equation (22). FIG. 13illustrates calculation of the groove. σx equals the length of ahypotenuse. α_(A) indicates the angle subtended by the hypotenuse withregard to the base of the waveguide. α_(c) is the total critical (TIR)angle of the light that is within the waveguide, approximately 40°. FIG.13 actually represents a worst case scenario for an extended source,assuming that no collimation was done between the source and its entryinto the waveguide. In FIG. 13, α_(c) is the angle between the incidentbeam on the reflective surface and the reflective beam, α_(c) being themaximum divergence within the waveguide. The grooves are designed forthe midpoint α_(c) /2. Equation (25) represents calculation of α_(A)based on α_(c). ##EQU10## Note that the maximum beam divergence can bereduced provided that collimation is achieved as light enters thewaveguide due to Snell's law. Nevertheless, α_(A) represents the optimumangle for splitting the flux represented by α_(c), or other maximumdivergence angle, smaller than α_(c). The typical index of refractionrange for the materials of interest is from 1.5 to 1.7, assuming arefractive index of 1.55. These materials include plastics, such as, forexample, acrylics such as polymethacrylate and polymethylmethacrylateand other polymers. Equation (26) assumes that the exterior medium isair having an index of refraction of 1 α_(c) /2 is approximately 40°under these conditions. ##EQU11## Thus, α_(A) equals approximately 35°based on this calculation as shown in Equation (26). Areas arerepresented in Equation (28), where a is the loss per groove. ##EQU12##Equation (28) represents that a percentage of the flux passing a pointis not going to intercept the hypotenuse, based on the hypotenuse beinga fraction of the total subtended length between the top of thewaveguide and the bottom of the waveguide. Total length of each groovehypotenuse is δx, assuming that the wave front of the waveguide ishomogenous. It should be noted that skew rays are being neglected. Thismodel is accurate within an order of magnitude. Assuming a width of 3mm, which is equal to D, refer now to Equation (29) where the width ofthe hypotenuse is determined as 8 microns. ##EQU13## 1/sin α_(A) is 1.7for the thickness of 3 mm, the leak per groove represented 3/2000,assuming a mirrored surface on the top. While each groove can be verysmall, but referring to FIG. 14, the corresponding lens needs to be muchlarger. FIG. 14 shows an imaging collimation slab located beneath acollimating waveguide. A gap of 1 micron between the two slabs is morethan sufficient to prevent undesired coupling between the structures,assuming 100 micron lens for example. The angle incident upon thecollimating imaging optic cannot be smaller than α_(c). Based on thepreviously assumed groove spacing of 3 mm, the resulting lens diameteris 2 mm, which is far too large. However, the grooves can be arranged inclusters permitting grouping. By grouping the grooves there can besufficient spacing for the imaging optics. The following examplerepresents an average distance of 2 mm between the clusters of grooves.N_(t) represents the number of clusters of grooves.

Δx=2 mm, L=20 cm, N_(t) =100, dx=160 μm

The smaller number of grooves is accounted for by a much larger δx. A δxof 160 microns corresponds to 1 microgroove per cluster. Increasing thenumber of microgrooves per cluster would reduce δx proportionally.However, N_(t) would remain at 100 representing the requirement for 100clusters of such microgrooves. In the following example, Δx is thedistance between clusters, and H is the lens diameter, and we assume,approximately, that H=Δx.

Δx=1 mm, L=20 cm, N_(t) =200

The size of the grooves can be varied much more and their geometricalposition can be cruder, therefore the grooves do not need to be prismsbecause the spherical rays are subsequently image collimated. Errorsfrom the microgroove surfaces can be accommodated with larger imagingoptics. In contrast, the prisms of U.S. Pat. Nos. 5,390,276 and5,359,691 are acting largely as mirrors and if there is distortion dueto imperfect structure the result will be divergence that the structuredisclosed in these patents will not subsequently correct for.

Collimation by a generalized wedge concept will now be described.Referring to FIG. 9, trigonometric relationship of the angle ofincidence α within this wedge will cause the angle of incidence to bereduced by 2γ after each bounce, assuming that γ is the wedge angle.Assuming the initial entry angle is approximately 40°, α will equal 50°.This is far larger than the critical angle so the first bounce will beby total internal reflection (TIR). At some point thereafter there willbe a bounce where some portion of the ray is leaked. Assuming the wedgeangle γ is 0.5°, 2γ is 1°, and in order to approach 40° a minimum of 10bounces is required, counting only the bounces from the bottom. Equation(49) describes the condition for leakage starting with an incident anglea and a wedge angle γ.

    α-N(2γ)=α.sub.cond                       (49)

The wedge has a sawtooth pattern. These sawtooths represent adistributed wedge. The upper section operates by total internalreflection (TIR) preferably, although the angled facet could bemetallized. The determination of the angle in the upper section is basedon the same bisectrix that was used to derive the angle of the curvedsurface. In general it will be appreciated that one facet should beapproximately vertical and the other approximately 45° in order to yielda straight-up normal collimated output. A monolithic wedge divided intoa series of solitudes can be characterized as a distributed wedge.

Referring to FIG. 10, a distributed wedge is shown. A distribution ofthe wedges provides a homogeneous illumination. This concept is similarto Equation (1). This derivation displayed ρ as a function of x holdingthe variable a constant. In the following derivation, the variable a isa function of x and ρ is constant. Alternatively, if the variable a isconstant and ρ is variable, the other derivation can be used. In thefollowing derivation P replaces I. P is the optical power. Equation(101) is the analog of Equation (1), except that the variable a is afunction of x and ρ is constant. ##EQU14## Equation (16) is identical toEquation (101) and Equation (17) sets a boundary condition. Equation(118) sets p x a equal to a constant A.

    dP=-Aρdx                                               (118)

Equation (123) should be compared to Equation (6). ##EQU15## It is clearthat in Equation (123) a is a function of x whereas in Equation (6) ρ isa function of x. A is a constant in both equations. In Equation (123) ais variable where ρ is constant. The variable a is the leakage rate permicroelement. ##EQU16##

Full Lambertian dispersion would be π/2. This can be reduced to 2β,where β is the critical angle from the previous interaction,approximately 40°, although it can be smaller assuming that somecollimation process has occurred before. It must be calculated what γshould be in order to obtain the desired leakage. Intensity is J=J_(o)cos α. While I is optical intensity and is expressed in units of wattsper square meter, for example, radiant intensity, J, is expressed inunits of watts per steradian. But in this derivation only the twodimensional case is being considered and J is expressed in watts perradian. Lambert's law is represented by J=J_(o) cos α. Integration inEquation (110) describes the total power going through the wave guidefrom -β to +β. ##EQU17## ΔP in Equation (113) is the leakage from 2γ.

    ΔP=2γ sinβ-sin(β--2γ)!         (113)

Assuming that γ is much less than 1 radian, this ΔP is used in thefollowing Equation (125): ##EQU18## Equation (126) describes relativeleakage for each event. In the distributed wedge the relative leakageper event is proportional to γ and fitting Equation (123) into Equation(126) yields Equation (128). ##EQU19## In Equation (128), γ is changingwith x according to the relationship shown in Equation (132). ##EQU20##As γ increases with x to provide constant leakage, it is enabled toregulate γ. Alternatively, ρ can be varied as was previously shown.Assuming density is constant at 10 per millimeter, ρ is constant asshown in Equation (136), ##EQU21## Assuming a total length L of 20 cm,Equation (137) shows that the leak per grove is small. ##EQU22##Equation (140) shows that the beginning angle only needs to be 1/10th ofa degree.

    2γ.sub.c =2·10.sup.-3 =0.1°          (140)

Again, the assumptions are ignoring skew rays. Illustrating skew rayswould only be possible with the fall ray tracing scheme program. Itwould be advantageous in order to accommodate skew rays to modify theorthogonal shapes to cylindrical symmetric shapes. This would involverepeating a cross section rotated around a vertical axis. Rotation canalso be based on an ellipse as opposed to a circle. In a (z,x) crosssection, the triangles are representing prisms, however, when consideredalong the (x,y) plane for the combination of skew rays, such triangularsections may actually become cones or more complex elliptical shapes inorder to accommodate the skew rays. Such a topology would be complex.

A more precise version of Equation (128) follows, including aconsideration of fresnel reflection, (represented by reflection(intensity coefficient) R as graphically depicted in FIG. 19), andmaterial absorption. The power p in Equation (128) is replaced byEquation (300):

    P→P(1-R-D)                                          (300)

Where R is Fresnel reflection coefficient, and D is absorptioncoefficient. Therefore, Equation (116) becomes:

    -dP=a(x)P(x) Δ-R(x)-D!ρdx                        (301)

Where D-coefficient is assumed to be constant, as well as ρ-coefficient.In order to preserve beam leak uniformity, the following Equation (302)should be satisfied:

    a(x)P(x) Δ-R(x) -D!=const.=A'                        (302)

Where A' is a new constant, analogous to the constant A. Using the samereasoning as above, the following Equation (303) is obtained fora-coefficient. ##EQU23## Equation (303) is identical to Equation (128),assuming R=D=O, and using the α-angle symbol instead of δ-angle. Forδ<<1, and α<<1, the relation between δ and γ is ##EQU24## Where Snell'slaw has been included. δ is the leakage angle and γ is the prism angle.This is shown in Table 1.

                  TABLE 1                                                         ______________________________________                                        LEAKAGE ANGLE 2δ VERSUS WEDGE ANGLE γ FOR n = 1.55,               γ  0.5°                                                                          1°    1.5°                                                                        2°                                   ______________________________________                                        2δ 11.6°                                                                         17.5° 21°                                                                         24.5°                                ______________________________________                                    

Table 1 illustrates that even for small γ-angles, δ-angles can be quitelarge. For angles, close to critical angle α_(c) (sin α_(c) =Δ/n), theFresnel reflection coefficients can be quite high. For example, forγ=0.2°, we obtain R=51%, while for γ=0.5°, R=30%.

As an example, an approximate solution of transcendental Equation (303)follows. Since R-coefficient depends on δ, Equation (303) is atranscendental one in such a sense that it cannot be solvedanalytically. In order to solve Equation (303) approximately, it isassumed, in the first iteration step, that an α_(L) -value (i.e.,γ-value, for x=L) equals 0.5°, which leads to the Fresnel reflectioncoefficient value: R=30%. It is further assumed that at the end of thewaveguide, 5% of light power remains; i.e., P(L)=0.05P_(o). Anabsorption coefficient value (conservative) of 2% is also assumed. Then,for n=1.55, and α_(c) =40°, α_(L) =0.74°. It will be appreciated thatthe first iteration step worked relatively well. Using Equation (304),δ=7° is obtained. Thus, the leakage angle (in the air) of 2δ is equal to14°. Of course, for x=0, the values of angles γ and δ (i.e., γ_(o) andδ_(o) -values) will be much smaller. Therefore, in this case, theγ-distribution is non-uniform. This numerical example demonstrates howto design the distributed wedge system. Its exemplary parameters havebeen summarized in Table 2.

                  TABLE 2                                                         ______________________________________                                        SUMMARY OF EXEMPLARY PARAMETERS OF THE                                        DISTRIBUTED WEDGE SYSTEM                                                      #   PARAMETER              SYMBOL   VALUE                                     ______________________________________                                        1   LENGTH                 L        20 cm                                     2   TOOTH DENSITY          σ  10/mm                                     3   WEDGE REFRACTIVE INDEX n        1.55                                      4   WAVEGUIDE THICKNESS    D        3 mm                                      5   POWER FRACTION AT THE END                                                                            P.sub.L /P.sub.o                                                                       0.05                                      6   WEDGE ANGLE AT x = L   γ.sub.L                                                                          0.74°                              7   MAXIMUM LEAKAGE ANGLE AT x = L                                                                       2δ.sub.L                                                                         14°                                ______________________________________                                    

Curved Facet Surfaces

Different parts of the surface of each facet are available to differentrays coining from different directions. Therefore, a flat surface facetis not always optimum because the available light is not ideallydistributed.

By ignoring skew rays, an optimized curved surface can be easilydesigned by assuming homogenous incident flux. For example, the bottomof an isosceles pit pyramid is not available to a low incident angleray. It is desirable to optimize the design of the facet so as to weightthe intensity of the flux cones that are available to any given surfaceof the reflection. For example, constructing an arc instead of aflattened prismatic surface reflecting rays coming from the leftrequires defining the maximum and minimum angles for those rays whichcan strike any part of the arc based on the geometry of the waveguide.More specifically, at the top of the arc waves cannot arrive at angleslower than 0° because they would be intercepted by the previous apex. Incontrast, at the bottom of the arc waves can arrive at a wider range ofangles. Referring to FIG. 16, bisecting the center of both of theseangles will result in a simple geometric definition of the tangent ofthe curve. However, the flux weighted center point of each of these twoangles will be slightly different from the geometric bisectrix becausethe waveguide is not homogeneously illuminated from the light source duethe light source itself generating a nonplanar, albeit somewhatsymmetric, flux distribution.

The curved tooth facet is mirrored and can be referred to as avignetting effect where there is a limited size and some parts of thebeam are blocked by structures. The first facet can be flat. Althoughit's shown as flat to facilitate analysis of the lowest-most ray, thefacet can actually be convex or concave. At the base of the apex, theangular spectrum is very limited. The widest angular spectra is at thetop, based on the incoming rays. The coordinate system labeled has itsorigin at the base of the structure. The problem is to find z as afunction of x for the curved surface.

Referring to FIG. 20, the sawtooth geometry, with curved surface 113 isdescribed, leading to the optimum curved surface z(x). This is a curvedsurface rather than a flat surface because the incident beams at pointsO, Q, P in FIG. 20, have increasing divergence as illustrated by thehatched areas in FIG. 20.

A description of FIG. 20 follows. FIG. 20 shows tooth 99. The vertex 100of the nonimaging optic(s) (NIO) tooth is O and is positioned followingbeam collimation optimization according to the Louiville theorem asgenerally explained by Wilford.sup.(1) and Winston.sup.(2).

Arbitrary point Q 101 is located on the curve: z=z(x), that should beoptimized. Of course, arbitrary point Q 101 has two coordinates (x,z).The highest point 102 on the curved wall is P. The height of the tooth103 is taken between P and O. The horizontal length of the straight wallis represented by 104. The z-coordinate of point Q is represented by105. Point Q is also origin of the coordinate system.

The lowest angle (α) of incident nays at point Q is represented by 106.The highest angle (β) of incident rays at point Q is represented by 107.This is also the maximum angle of beam divergence. As a result of totalinternal reflection (TIR) inside collimating waveguide, the maximumvalue of angle β is: ARC TAN (1/n), where n is reflective index of thetooth which is surrounded by air. For n=1.55, β≈40°.

A bisect angle, equal to ##EQU25## is represented by 108. The incidentangle (α) of bisect ray, which is a central ray for the beam (or, raybundle) approaching point Q, is represented by angle 109. Angle 110 isthe reflection angle of bisect ray and is equal to angle 109. 111represents the symmetrical angle (δ) for bisect rays. It should be notedthat symmetrical line 119 is perpendicular to tangential line 114.Therefore, the tangential angle is 90°-δ (or, π/2-δ).

112 is a straight line (or, wall in cylindrical geometry) of the tooth.113 is the tooth curve that characterizes the optimum NIO profile,minimizing divergence of the output beam. This is because, by contrastto the prism, the ray-bundle at any point at the surface is reflectedsymmetrically into vertical direction. This is due to the fact that thebisect line of any ray bundle is reflected exactly vertically.

114 is the tangential line into the curve at point Q. 115 is theincident ray at point O. This is the maximum divergence ray. 116 is thelowest inclination ray for the ray bundle at point Q. 117 is the highestinclination ray at point Q. 118 is the bisect ray for the ray bundle atpoint Q. 119 is the symmetrical line to bisect incident ray 118 andbisect reflected ray 120, which is precisely perpendicular to tangentialline 119.

120 is the reflected ray into incident bisect ray 118 which is preciselyvertical, or parallel to z-axis. 121 is the reflected ray to incidentray 115 which is also precisely vertical, according to the optimizationprinciple. 122 is the lowest inclination incident at highest Point P,which has a horizontal direction. 123 is the highest inclination whichis assumed to be β, in order to accommodate the maximum amount of rays.124 is the bisect ray at point P. 125 is the reflected ray to bisect ray114 which is always precisely vertical, according to the optimizationprinciple.

An analytical procedure for defining the optimized curve z =z(x)follows. According to FIG. 20, the angle 111, or δ, is ##EQU26## Where αis angle 106 and β is angle 107. It should be noted, that, whileaccording to the optimization principle, β-angle is constant, for anypoint Q at the curve, α-angle is defined as follows: ##EQU27## i.e., αis a function of z-coordinate. Thus, the δ-angle is also a function ofz. Therefore, line 113 is not straight but curved, according to theoptimization principle; and ##EQU28## The basic differential equationdefining the optimization principle is ##EQU29## Where dx and dz areinfinitesimal changes or coordinates (x,z), at point Q of the curveusing Equations (202), (203), (204) and (205), we obtain, ##EQU30## andthe solution of the problem, is ##EQU31## Typically, the solution ispresented in the inverse form to Equation (207): ##EQU32##

The Equation (208) can be numerically calculated for various values of Gand angles β. A calculation and illustration for two-cases of curvez(x), where x(z) is determined by Equation (207) as shown in FIG. 21follow.

FIG. 21 shows a multiplication of the optical element shown in FIG. 20for unidirectional illumination. FIG. 25 is a generalization of FIG. 24for bi-directional illumination.

Referring to FIG. 22, a calculation and illustration of the sawtoothdesign for the case: G=100 μm,β=40° is shown. We see that the surface113 is indeed curved. The single sawtooth element from FIG. 22 has beenillustrated in detail in FIG. 23 and multiplied in FIG. 24 in order toshow a practical sawtooth applied to one side of the collimatingwaveguide as in FIG. 15. In order to apply two sources from both sidesof the waveguide, the curved surface 113 has been applied on both sidesin FIG. 25. It should be noted that skew rays have not been consideredin this analysis, for simplicity. In FIG. 26, the structure from FIG. 25is depicted with smooth lower vertices, in order to minimize thescattering at the edges.

The shape of the curve in the vignetting effect curved tooth is afunction not only of the geometry of the chasm defined by the firstfacet and the second facet of each optical element but also the outputof the light engine. Thus, it is useful to consider the flux dispersionof the light engine and the flux dispersion within the collimatingwaveguide.

Fabrication of Collimating Waveguide

Conveniently, the collimating waveguides of the present invention can becarried out by using any fabrication method. For the manufacturingoperation, it is moreover an advantage to employ areplication/lamination method.

Isosceles triangles can be cut when fabricating the master forreplicating the collimating waveguide provided that there is noundercutting. Any undercutting inhibits mold release. There is a generaldegradation as you move from the master to the submaster to the finishedpart. Degradation removes the edges. Much of this degradation is due tothe forces exerted during release. Thus, the shape on the master is notnecessarily the finished facet structure. Although the facets themselvestend to become convex due to the release process, concave shapes arepossible to make. Further, it is relatively easy to combine two facetsto define a compound concave structure.

To fabricate the master for the above-discussed assemblies of opticalelements, a metal master can be machined with diamond tooling. Machiningflat facet microgrooves with cylindrically variable angles is possible.A spherical or aspheric curve can be cut on a diamond and the resultingcurved optical microelement could be as small as 50 microns. Variableangles are possible with curved facets as well. Variable spacing ispossible with both flat facets and curved facets. In addition, imagingmicrolenses can be cut as small as 200 microns. However, the diamondtooling wears-out so it is advantageous to fabricate one master and thenreplicate a series of submasters.

Liquid Crystal Displays

Liquid crystal displays can be high definition and/or low definition.The number of pixels can be, for example, 2000×2000. Presently thesmallest size pixel resolution is approximately 20 microns. These LCDsproduce undesirable pixeling effect. Viewers can actually see thesepixel demarcations.

Diffusers

An important function that can be carried out by a diffuser locatedbetween the collimating waveguide and the LCD is to cancel pixelingeffect from the LCD. Such a use of a diffuser can be termedhomogenizing.

In addition, the directionality of the light emitted from the LCD can beoptimized through the use of a diffuser with directional characteristicslocated on top of the LCD. This would allow a private limited viewingrange from a laptop computer. Directional diffusers are non-Lambertiandiffusers, optical properties of which are defined by planewave responseas discussed in U.S. Pat. No. 5,365,354. It can be assumed that theincident waves are not fully collimated but have divergence of perhaps±10°. Of course, the divergence from the diffuser cannot be less thanthe divergence that is reaching it. Typical values would be fromapproximately 1-40° half angle. As a practical matter, if the incidentdivergence is approximately 20° and the divergence of the diffuser isapproximately 1° then the output would be approximately the same as theinput with regard to divergence. Diffusers do not help in collimation.However, diffusers most definitely help in homogenization. Specifically,such diffusers can obviate pixeling from the LCD.

A diffuser can be located between the groove structure and the LCDstructure and/or a diffuser can be located after the LCD. In the formercase, the diffuser will homogenize only the grid structure and not thepixels. In the latter case the diffuser would be homogenizing bothstructures.

Diffuser Fabrication

Methods for making the light shaping holographic surface reliefdiffusers of the present invention are now described. Generally, thefirst step is to create a master diffuser, the second step is to recordin a photosensitive medium with coherent light passed through the masterdiffuser, and the third step is to replicate the surface structure ofthe photosensitive medium with, for example, epoxy. A fourth andoptional step is to make a metal electroform master from the epoxy formass production purposes. In the alternative, an electroform master maybe made directly from the master diffuser.

Referring to FIG. 18, a recording set-up 16 is shown comprising acoherent laser light source 18, objective lens 200, master diffuser 22,and photosensitive medium 24. Coherent laser light source 18 isstandard. The objective lens 200 is standard and may be a low or highmagnification lens depending upon the desired characteristics of thephotosensitive medium 24. The objective lens is spaced a distance X fromthe master diffuser 22. The master diffuser 22 may comprise a standardground glass diffuser, a lenticular diffuser, an acetate diffuser, or aholographic diffuser. The ground glass, lenticular, and acetatediffusers are conventional and made in a conventional manner. If aholographic master diffuser is desired to be used, that master diffusermay itself first be recorded in the recording set-up shown in FIG. 18with the holographic master diffuser to be recorded being positioned at24 and a conventional ground glass diffuser being located at 22. Thatmaster diffuser may then be used to record into another photosensitivemedium to be used as a light shaping holographic surface relief diffuseraccording to the present invention.

A related set-up for recording volume holographic diffusers is describedin U.S. Pat. No. 5,365,354. According to that disclosure, recording aholographic plate with coherent laser light passed through aconventional ground glass diffuser generates features called speckle inthe volume of the hologram. The size, shape, and orientation of thespeckle can be adjusted which in turn affects the angular spread oflight scattered from the holographic diffuser upon playback. Generally,the size of the angular spread of the scattered light, in other words,the angular distribution of the scattered light, depends on the averagesize and shape of the speckle. If the speckle are small, angulardistribution will be broad. If the speckle size is horizontallyelliptical, the shape of the angular distribution will be verticallyelliptical. Thus, it is desirable to control the size and shape ofspeckle recorded in the medium so that, upon playback, the correctoutput or angular spread is produced.

Speckle size is inversely proportional to the size of the aperture ofthe master diffuser. If the size of the aperture increases, the size ofthe speckle decreases and the size of the angular spread of thescattered light from the recorded photosensitive medium increases.Conversely, if the size of the master diffuser aperture decreases, thesize of the speckle recorded in the diffuser increases and the angularspread of light scattered from the recorded photosensitive mediumdecreases. Thus, if the master diffuser aperture is long and narrow, thespeckle will be long and narrow as well with their axes orientedperpendicularly to the axis of the aperture. This holds true for bothvolume holographic recording media as well as surface holographicrecording media.

Diffusers made from volume holographic recording media as in U.S. Pat.No. 5,365,354, however, are disclosed there for their volume effect. Inother words, the speckle recorded in the interior or volume of themedium was thought the only desired effect to be obtained from thematerial. However, since then we have discovered that recording a volumeholographic angular spread such as DCG (dichromated gelatin) in asimilar recording set-up produces a surface effect of peaks and valleyswhich may be replicated as described below.

The size, shape, and orientation of the surface features recorded inphotosensitive medium 24 is a function of a number of variablesincluding the type of objective lens 200 and master diffuser 22 used, aswell as the relative positioning of those components with respect toeach other and with respect to the photosensitive medium 24. Ultimately,the desired results are obtained through empirical testing. In order toachieve a recorded photosensitive medium having a particular surfacestructure that can be replicated and comprise a light shapingholographic surface relief diffuser according to the present invention,it may be necessary to adjust the parameters discussed below to achievethe desired shape of the light output.

The objective lens 200 expands the coherent laser light source 18 sothat the area of incidence (or "apparent aperture") of light from theobjective lens 200 on the master diffuser 22 is larger than that of thecross section of the laser beam itself. The light beam expands inaccordance with the magnification of the objective lens 200.

Consequently, if a small magnification objective lens is used, such as5×, the aperture of light incident the master diffuser 22 will besmaller than with a large magnification objective lens, such as 60× orgreater, and therefore the size of the surface features recorded in thephotosensitive medium 24 will be larger; the size of the aperture oflight incident the master diffuser 22 is inversely related to the sizeof the surface features recorded in the photosensitive medium 24.

The distance between the objective lens 200 and the master diffuser 22must also be taken into account in achieving the desired sculptedsurface structure recorded in the photosensitive medium 24. As thedistance between the objective lens 200 and the master diffuser 22decreases, i.e., as X decreases, the size of the speckle increases. Thisoccurs because as the objective lens 200 moves closer to the masterdiffuser 22, the apparent aperture of light incident the master diffuser22 is smaller. Because the size of the speckle recorded in thephotosensitive medium 24 is inversely related to the size of theapparent aperture on the master diffuser 22, the speckle will be larger.In turn, the increased speckle size recorded in the photosensitivemedium 24 will result in a light shaping holographic surface reliefdiffuser which has decreased diffusion.

Conversely, if the distance X is increased, the apparent aperture oflight incident the master diffuser 22 will increase, thus decreasing thesize of the speckle recorded in the photosensitive medium 24 and in turnincreasing the amount of angular spread of the light shaping holographicsurface relief diffuser.

The distance Y between the master diffuser 22 and the photosensitivemedium 24 also affects speckle size. As the distance Y decreases, thesize of the speckle recorded in the photosensitive medium 24 decreasesas well. This occurs because, assuming an expanded beam of light isproduced at objective lens 200, as the photosensitive medium 24 is movedcloser to the master diffuser 22, the light beam emanating from each ofthe irregularities in the master diffuser 22 will expand less by thetime it reaches the photosensitive medium 24, thus producing smallerspeckle. Conversely, if the distance Y is increased, the size of thespeckle recorded will be increased. Thus, these simple relationshipsbetween the distances X, Y, and the magnification of the objective lens200, are all adjusted, empirically, to achieve the size of speckledesired in the photosensitive medium 24.

Predefined output areas that are "off-axis" with respect to the normalaxis of the diffuser are achieved by tilting the photosensitive medium24 around an axis normal to its surface. For example, a 20° off axisdiffuser may be achieved by fitting the photosensitive medium 24 roughly20°.

Assuming that a ground glass diffuser is used as the master diffuser 22,the shape of the speckle recorded in photosensitive medium 24 will beroughly round as will the shape of the angular output of a light shapingholographic surface relief diffuser made from photosensitive medium 24.A round output may also be achieved when a lenticular or an acetatesheet is used as a master diffuser 22. Lenticular sheets have tinylens-like elements machined in them. Acetate diffusers are made by anextrusion and embossing process which also yields roughly round speckle.It is difficult to create or control the desired irregularities inacetate diffusers. With respect to lenticular diffusers, the surfaceeffects necessary to achieve varying output shapes are complex machinedmacroscopic structures. If a prerecorded holographic master diffuser isused as the master diffuser 22, additional degrees of recording freedomare achieved because the master diffuser can be prerecorded with specklehaving virtually any shape, size, and orientation as discussed furtherbelow. Speckle characteristics are more easily controlled using aholographic master diffuser.

In any case, in the recording set-up in FIG. 18, the master diffusermust be able to transmit light so that it reaches the photosensitivemedium 24 from the objective lens 200. Thus, if a substrate is needed aspart of the master diffuser 22, such as if a holographic master diffuseris used, the substrate should be capable of efficiently transmittinglight. A glass substrate is preferable. In addition to the additionaldegrees of freedom which can be achieved by using a prerecorded volumeor surface hologram as the master diffuser 22, holographic masterdiffusers are preferable because better uniformity of intensity in thephotosensitive medium 24 is achieved, higher transmission efficiencythrough the master diffuser 22 is achieved, and the holographic masterdiffuser 22 causes less back scatter than a ground glass diffuser. Afirst generation holographic volume master diffuser may be made using aground glass or acetate diffuser. This holographic diffuser can then beused to make a second generation holographic master diffuser, eithervolume or surface with greater control.

3. DESCRIPTION OF SPECIFIC EMBODIMENTS

Referring to FIG. 5, light source 60 is located within space defined bymirror 70. Light source 60 can be a cold cathode fluorescent bulb or ahot cathode fluorescent bulb. Light from light source 60 is directedtoward waveguide collimator 80. Light source 60 is connected to mirror70 through fixture 90.

Light source 60 can be more generally referred to as an illuminationsource. Waveguide collimator 80 includes incident end 130. The bottom ofwaveguide collimator 80 is provided with a first plurality ofsubstantially parallel optical elements 140. Each of the first pluralityof substantially parallel optical elements 140 includes a first facet142 and a second facet 144. Waveguide collimator 80 includes a topsurface 146. Waveguide collimator 80 can also include a reflective end(not shown).

Referring to FIG. 6, light engine 1100 is connected to waveguidecollimator assembly 108. Light source 1200 is a linear array of lightemitting diodes connected to a metallized mirror that is part of lightengine 1100.

With regard to the examples shown in FIGS. 5 and 6, and the otherembodiments, light from the illumination source can be directly incidentupon the incident end. This means that there is no structure between theillumination source and the incident end. For example, the space betweenthe illumination source and the incident end should be occupied by air,or vacuum. By the absence of any structure between the illuminationsource and the incident end, a higher degree of collimation is achievedwhen light passes through the incident end in accordance with Snell'slaw.

Referring to FIG. 11, first distributed wedge collimating waveguide 150includes a first plurality of substantially parallel optical elements160. Each of this first plurality of substantially parallel opticalelements 160 includes a first facet 162 that can be substantially flatand a second facet 164 that can be substantially flat. First distributedwedge collimating waveguide 150 also includes top surface 166. The angleγ which is defined as the angle that the first facet 162 makes with thetop surface 166 should be optimized. Second distributed collimatingwaveguide 170 is optically connected to first distributed wedgecollimating waveguide 150. Second distributed wedge collimatingwaveguide 170 includes upper surface 172. First diffuser 180 forhomogenizing light from upper surface 172 is optically connected tosecond distributed wedge collimating waveguide 170.

An additional collimating waveguide including a plurality of imagingoptics can be located between first diffuser 180 and second distributedwedge collimating waveguide 170. In addition, a diffuser can be locatedadjacent incident end 168.

FIG. 12 shows a ray diagram for the apparatus depicted in FIG. 11. Atthe left of FIG. 12, a ray is leaked at near zero degree angle to thetop surface. It will be appreciated that this ray is emitted from thetop of the diffuser toward the left. In the middle of FIG. 12, a ray isemitted from the top surface at an angle γ. This ray emerges normal tothe plane defined by the diffuser. Toward the right of FIG. 12, a rayemerges from the top surface at an angle to γ. It will be appreciatedthat this ray is emitted from the diffuser toward the right.

Referring to FIG. 14, first collimating waveguide 190 is provided with afirst plurality of substantially parallel optical elements 195. Each ofthe first plurality of substantially parallel optical elements 195includes a mirrored first facet 197 and a second facet 198. Firstcollimating waveguide includes a top surface 196 and an incident end(not shown). Second collimating waveguide 210 is optically connected tothe top surface 196. Second collimating waveguide 210 is provided with aplurality of substantially parallel imaging optics 220. Secondcollimating waveguide 210 includes upper surface 215.

Referring to FIG. 15, first collimating waveguide 230 includes topsurface 231. First collimating waveguide 230 also includes an incidentend (not shown) and a reflective end (not shown). First collimatingwaveguide 230 is provided with a first plurality of substantiallyparallel optical elements 240. Each of the first plurality ofsubstantially parallel optical elements 240 includes a first facet 242and a mirrored second facet 244. Second facet 244 is concave withrespect to top surface 231. Although it is not shown, first facet 242can also be concave with respect to top surface 231.

Referring to FIG. 16, a graphical construction illustrating the propertangent for any point on second facet 244 is provided. It will beappreciated that the angle S defined by first facet 242 is equivalent tothe angular dispersion of the rays incident upon mirrored second facet244 at the point being considered.

Referring to FIGS. 17A-17C the aspect ratio of the base of the elementsis proportional to the ratio of divergence of the beams in horizontaland vertical.

Referring to FIG. 17A, a first plurality of substantially paralleloptical elements having concave facets have been replicated in a firstcollimating waveguide. It will be appreciated that the first pluralityof substantially parallel optical elements are not continuous but ratherhave been segmented into a series of microchasms.

Referring to FIG. 17B, a second plurality of substantially parallelimaging optics are shown replicated in a second collimating waveguide.It will be appreciated that the second plurality of substantiallyparallel optical elements have been segmented into spherically symmetricindentations.

Referring to FIG. 17C, a first plurality of substantially paralleloptical elements formed in a first collimating waveguide is shown. Thefirst plurality of substantially parallel optical elements have mirroredfirst facets that are concave and mirrored second facets that areconcave. It will be appreciated that concavity of the facets has beenthree dimensionally deviated so as to define scalloped edges so as tocollimate skew rays.

For electrical purposes one light source is often preferred. This alsoallows for a more compact structural design. However, the use of twosources can be conjunctively combined with an optical element havingopposed concave surfaces so as to preferentially direct flux upwardwhere the flux is incident from both sides of the waveguide collimator.This opposed concave configuration is also applicable to the case whereone light source is used in conjunction with a mirror on the reflectiveend of the collimating waveguide. For ease of manufacture a symmetricalidentical backside is preferred. This will also effectively collimatemuch of the backscattered light. However, depending on the geometry, theback surface can be concave in a different configuration from the frontsurface.

Preferred embodiments of the present invention can be identified one ata time by testing for the presence of collimated output. The test forthe presence of collimated output can be carried out without undueexperimentation by the use of the simple and conventional polarizationexperiments. Among the other ways in which to seek embodiments havingthe attribute of collimated output, guidance toward the next preferredembodiment can be based on the presence of homogeneity.

The disclosed embodiments show a fluorescent bulb as the structure forperforming the function of emitting light, but the structure foremitting light can be any other structure capable of performing thefunction of emitting light, including, by way of example an array oflight emitting diodes (LEDs), or any other non-monochromatic lightsource, such as a strobe light. The illumination source can even be amonochromatic light source, albeit less commercially viable.

The disclosed embodiments show cylindrical and conical microlenses asthe structures for performing the function of imaging collimation, butthe structure for imaging collimation can be any other structure capableof performing the function of changing the divergence light, including,by way of example a nonlinear optic such as a convection chamber.

The disclosed embodiments show a light shaping diffuser as the structurefor performing the function of shaping light, but the structure forshaping light can be any other structure capable of performing thefunction of shaping light, including, by way of example, a lens such asa Fresnel lens.

A practical application of the present invention which has value withinthe technological arts is illuminating a liquid crystal display.Further, all the disclosed embodiments of the present invention areuseful in conjunction with liquid crystal displays such as are used forthe purpose of displaying data, or for the purpose of displaying animage, or the like. There are virtually innumerable uses for the presentinvention described herein, all of which need not be detailed here.

The present invention described herein provides substantially improvedresults that are unexpected in that a very good output is obtained withrelatively low power. The present invention described herein can bepracticed without undue experimentation. The entirety of everythingcited above or below is hereby expressly incorporated by reference.

Although the best mode contemplated by the inventors of carrying out thepresent invention is disclosed above, practice of the present inventionis not limited thereto. It will be manifest that various additions,modifications and rearrangements of the features of the presentinvention may be made without deviating from the spirit and scope of theunderlying inventive concept.

For example, the compactness of the system could be enhanced byproviding thinner illumination sources or thinner collimatingwaveguides. Similarly, although plastic is preferred for the collimatingwaveguide, any optically refractive material could be used in its place.In addition, the rest of the individual components need not befabricated from the disclosed materials, but could be fabricated fromvirtually any suitable materials.

Moreover, the individual components need not be formed in the disclosedshapes, or assembled in the disclosed configuration, but could beprovided in virtually any shape, and assembled in virtually anyconfiguration, which collimate light so as to provide backlighting.Further, although the liquid crystal display system described herein isa physically separate module, it will be manifest that the liquidcrystal display may be integrated into the apparatus with which it isassociated. Furthermore, all the disclosed features of each disclosedembodiment can be combined with, or substituted for, the disclosedfeatures of every other disclosed embodiment except where such featuresare mutually exclusive.

It is intended that the appended claims cover all such additions,modifications and rearrangements. Expedient embodiments of the presentinvention are differentiated by the appended subclaims.

REFERENCES

1. W. T. Welford and R. Winston, Optics of Nonimaging Concentrators,Academic Press (1978).

2. R. Winston and T. Jannson, Liouville Theorem and Concentrator Optics,Journal of Optical Society of America A, 3, 7 (1986) and Journal ofOptical Society of America A1, 1226 (1984).

What is claimed is:
 1. An apparatus, comprising:an illumination sourcefor producing light; a first collimating waveguide optically connectedto said illumination source, said first collimating waveguide includinga top surface, an incident end and a first plurality of substantiallyparallel optical elements for redirecting light from said incident endto, and through, said top surface by total internal reflection, each ofsaid first plurality of optical elements including a concave first facetthat is nonparallel to said top surface and a second facet that isnonparallel to said top surface, said second facet being concave withrespect to said top surface; a second collimating waveguide opticallyconnected to said first collimating waveguide, said second collimatingwaveguide including an upper surface and a second plurality of opticalelements for redirecting light from said top surface through said uppersurface; a diffuser for homogenizing light optically connected to saidsecond collimating waveguide; and a reflector optically connected tosaid light source and optically connected to said first distributedwedge collimating waveguide, said reflector (1) at least partiallysurrounding said illumination source, and (2) reflecting light from saidillumination source to said incident end by direct reflection.
 2. Theapparatus of claim 1, further comprising a nonimaging optic between saidillumination source and said incident surface, said nonimaging opticbeing optically connected to said illumination source and said firstcollimating waveguide.
 3. The apparatus of claim 1, wherein saiddiffuser includes a light shaping holographic surface diffuser having atleast one diffuser characteristic selected from the group consisting ofdirectional and off-axis.
 4. A backlight comprising:a collimatingwaveguide having a light input end, a top surface, a bottom surface, andopposing sides;said bottom surface converging toward said top surface ina direction along said backlight away from said light input end; saidbottom surface comprising a plurality of straight facets having adensity ρ distributed along said bottom surface in a direction alongsaid backlight away from said light input end and extending at leastpart way between said opposing sides; each said straight facet having astraight facet bottom surface which converges toward said top surface ina direction along said backlight away from said light input end at anangle γ less than approximately 5°; each said straight facet bottomsurface of each said straight facet being parallel to each said straightfacet bottom surface of each other said straight facet; said collimatingwaveguide reflecting light rays entering said light input end inaccordance with total internal reflection and entering with an anglegreater than said total internal reflection critical angle; said facetscausing light rays entering said light input end and having an anglenear said total internal reflection critical angle to exit said topsurface at an angle nearly tangential to said top surface.
 5. Thebacklight of claim 4, wherein said facets cause light rays entering saidlight input end and having an angle near said total internal reflectioncritical angle to exit said top surface at an angle of approximately 2γ.6. The backlight of claim 4, wherein each said straight facet bottomsurface is reflective to prevent light from leaking from each saidstraight facet bottom surface.
 7. The backlight of claim 4, wherein eachsaid straight facet bottom surface is metalized to prevent light fromleaking from each said straight facet bottom surface.
 8. The backlightof claim 4, wherein light leaks from each said straight facet bottomsurface and from said top surface.
 9. The backlight of claim 4, whereineach said straight facet extends between said opposing sides.
 10. Thebacklight of claim 4, wherein said density ρ of said straight facetsvaries as a function of a distance from said light input end.
 11. Thebacklight of claim 10, wherein said density ρ of said straight facets issuch that an intensity of emitted light is uniform across a length ofsaid backlight.
 12. The backlight of claim 10, wherein each saidstraight facet bottom surface is metalized to prevent light from leakingfrom each said straight facet bottom surface.
 13. The backlight of claim4, further comprising a diffuser optically coupled to said top surfacefor homogenizing light exiting said top surface.
 14. The backlight ofclaim 13, further comprising a non-Lambertian second diffuser opticallycoupled to said light input end for reducing reflection from said lightinput end.
 15. The backlight of claim 4, further comprising anon-Lambertian diffuser optically coupled to said light input end forreducing reflection from said light input end.
 16. The backlight ofclaim 4, further comprising a liquid crystal display optically coupledto said collimating waveguide.
 17. The backlight of claim 16, furthercomprising a non-Lambertian diffuser optically coupled to said liquidcrystal display for directing light from said liquid crystal display.18. The backlight of claim 17, further comprising a second diffuseroptically coupled to said top surface for homogenizing light exitingfrom said top surface.
 19. The backlight of claim 18, further comprisinga non-Lambertian third diffuser optically coupled to said light inputend for reducing reflection from said light input end.
 20. The backlightof claim 4, further comprising a spatial light modulator opticallycoupled to said collimating waveguide.
 21. The backlight of claim 4,further comprising a light source optically coupled to said light inputend.
 22. The backlight of claim 21, further comprising a reflectoroptically coupled to said light source and optically coupled to saidlight input end of said collimating waveguide, said reflector at leastpartially surrounding said light source and reflecting light from saidlight source to said light input end by direct reflection, wherein lightfrom said reflector is directly incident upon said light input end. 23.The backlight of claim 4, further comprising a second collimatingwaveguide optically coupled to said collimating waveguide, said secondcollimating waveguide including an upper surface and a second pluralityof facets for redirecting light exiting said top surface through and outsaid upper surface at an angle substantially greater than 2γ andapproximately normal to said top surface.
 24. A backlight comprising:acollimating waveguide having a light input end, a top surface, a bottomsurface, and opposing sides;said bottom surfaces converging toward saidtop surface in a direction along said backlight away from said lightinput end; said bottom surface comprising a plurality of straight facetshaving a density ρ distributed along said bottom surface in a directionalong said backlight away from said light input end and extending atleast part way between said opposing sides; each said straight facethaving a straight facet bottom surface which converges toward said topsurface in a direction along said backlight away from said light inputend at an angle less than approximately 5°; each said straight facetbottom surface of each said straight facet being parallel to each saidstraight facet bottom surface of each other said straight facet; saidcollimating waveguide reflecting light rays entering said light inputend in accordance with total internal reflection and at an angle greaterthan a total internal reflection critical angle; said facets causinglight entering said light input end and having an angle near said totalinternal reflection critical angle to exit said top surface at an anglenearly tangential to said top surface and of approximately 2γ; a secondcollimating waveguide optically coupled to said collimating waveguide,said second collimating waveguide including an upper surface and asecond plurality of facets for redirecting light exiting said topsurface through and out said upper surface at an angle substantiallygreater than 2γ and approximately normal to said top surface; anon-Lambertian diffuser optically coupled to said second collimatingwaveguide for directing light exiting said second collimating waveguide.25. The backlight of claim 24, wherein said non-Lambertian diffuserprovides a controllable output angle determined by surface featuresreplicated in said non-Lambertian diffuser from speckle recorded in aphotosensitive medium which determine angular output characteristics ofsaid non-Lambertian diffuser.
 26. The backlight of claim 24, whereinsaid second collimating waveguide is integral with said non-Lambertiandiffuser.
 27. The backlight of claim 25, wherein γ is in the range0.5°-2.0°.
 28. A backlight comprising:a collimating waveguide having alight input end, a top surface, a bottom surface, and opposingsides;said bottom surfaces converging toward said top surface in adirection along said backlight away from said light input end; saidbottom surface comprising a plurality of straight facets distributedalong said bottom surface in a direction along said backlight away fromsaid light input end and extending at least part way between saidopposing sides; each said straight facet having a straight facet bottomsurface arranged substantially parallel to said bottom surface whichconverges toward said top surface in a direction along said backlightaway from said light input end at an angle less than approximately 5°;and wherein said straight facet bottom surfaces cause light raysentering said light input end and having an angle near said totalinternal reflection critical angle to exit said top surface at an anglenearly tangential to said top surface.
 29. The backlight of claim 28,wherein said bottom surface converges toward said top surface at anangle between 0.5° to 2.0°.
 30. The waveguide of claim 28 wherein saidcollimating waveguide reflects light rays entering said light input endin accordance with total internal reflection and at an angle greaterthan a total internal reflection critical angle.
 31. The waveguide ofclaim 28 wherein said straight facet bottom surfaces cause light raysentering said light input end and having an angle near said totalinternal reflection critical angle to exit said top surface at an angleto said top surface and of approximately 2γ.
 32. The waveguide of claim28, wherein the facets have an density distribution along said bottomsurface that varies as a function of a direction along said backlightaway from said light input end.
 33. The waveguide of claim 28, whereineach said straight facet bottom surface of each said straight facet isparallel to each said straight facet bottom surface of each other saidstraight facet.
 34. The backlight of claim 28, wherein said facets causelight rays entering said light input end and having an angle near saidtotal internal reflection critical angle to exit said top surface at anangle of approximately 2γ.
 35. The backlight of claim 28, wherein eachsaid straight facet bottom surface is reflective to prevent light fromleaking from each said straight facet bottom surface.
 36. The backlightof claim 28, wherein each said straight facet bottom surface ismetalized to prevent light from leaking from each said straight facetbottom surface.
 37. The backlight of claim 28, wherein light leaks fromeach said straight facet bottom surface and from said top surface. 38.The backlight of claim 28, wherein each said straight facet extendsbetween said opposing sides.
 39. The backlight of claim 28, wherein saiddensity ρ of said straight facets varies as a function of a distancefrom said light input end.
 40. The backlight of claim 39, said density ρof said straight facets is such that an intensity of emitted light isuniform across a length of said backlight.
 41. The backlight of claim39, wherein each said straight facet bottom surface is metalized toprevent light from leaking from each said straight facet bottom surface.42. The backlight of claim 28, further comprising a diffuser opticallycoupled to said top surface for homogenizing light exiting said topsurface.
 43. The backlight of claim 42, further comprising anon-Lambertian second diffuser optically coupled to said light input endfor reducing reflection from said light input end.
 44. The backlight ofclaim 28, further comprising a non-Lambertian diffuser optically coupledto said light input end for reducing reflection from said light inputend.
 45. The backlight of claim 28, further comprising a liquid crystaldisplay optically coupled to said collimating waveguide.
 46. Thebacklight of claim 28, further comprising a non-Lambertian diffuseroptically coupled to said liquid crystal display for directing lightfrom said liquid crystal display.
 47. The backlight of claim 46, furthercomprising a second diffuser optically coupled to said top surface forhomogenizing light exiting from said top surface.
 48. The backlight ofclaim 47, further comprising a non-Lambertian third diffuser opticallycoupled to said light input end for reducing reflection from said lightinput end.
 49. The backlight of claim 28, further comprising a spatiallight modulator optically coupled to said collimating waveguide.
 50. Thebacklight of claim 28, further comprising a light source opticallycoupled to said light input end.
 51. The backlight of claim 39, furthercomprising a reflector optically coupled to said light source andoptically coupled to said light input end of said collimating waveguide,said reflector at least partially surrounding said light source andreflecting light from said light source to said light input end bydirect reflection, wherein light from said reflector is directlyincident upon said light input end.
 52. A backlight comprising:acollimating waveguide having a light input end, a top surface, a bottomsurface, and opposing sides, said bottom surface converging toward saidtop surface in a direction along said backlight away from said lightinput end, said bottom surface comprising a plurality of curved facetsdistributed along said bottom surface in a direction along saidbacklight away from said light input end and extending at least part waybetween said opposing sides, each said curved facet having a curvedfacet bottom surface, each said curved facet bottom surface beingarranged to reflect a ray-bundle incident to said curved facet bottomsurface, and wherein said ray-bundle comprises a plurality of light raysand wherein each of said light rays is reflected substantially normallyto the top surface in a symmetrical distribution.
 53. The backlight ofclaim 52, wherein said plurality of curved facets are arranged in anarray distributed on said bottom surface.
 54. The backlight of claim 52,wherein said plurality of curved facets are arranged in a segmentedarray.
 55. The backlight of claim 52, wherein said plurality of curvedfacets are arranged into segments, each said segment being arrangedparallel to each other said segment.
 56. The backlight of claim 52,wherein said plurality of curved facets are distributed with anincreasing density ρ from said light input end.
 57. The backlight ofclaim 52, wherein said density ρ of said straight facets is such that anintensity of emitted light is uniform across a length of said backlight.58. The backlight of claim 27, wherein each of said plurality of curvedfacets are concave with respect to said top surface.
 59. The backlightof claim 54, wherein said bottom surface converges towards said topsurface at an angle less than about 5°.
 60. The backlight of claim 54,wherein said bottom surface converges toward said top surface at anangle of about 0.50°-2.0°.
 61. The backlight of claim 54, wherein saidcollimating waveguide further comprises a second light input endopposing said light input end, said bottom surface further comprising aplurality of second curved facets each opposing said plurality of curvedfacets and each having a second curved facet bottom surface, each saidsecond curved facet being arranged to reflect a second ray-bundleincident to said second curved facet bottom surface, and wherein saidsecond ray-bundle comprises a plurality of light rays and wherein eachof said light rays are reflected substantially normally to the topsurface and in a symmetrically distribution.
 62. The backlight of claim61, wherein each said second curved facet is concave with respect tosaid top surface.
 63. The backlight of claim 61, wherein each saidcurved facet and each said second curved facet is concave with respectto said top surface.
 64. The backlight of claim 61, wherein each saidcurved facet and each said second curved facet is arranged withscalloped edges, said scalloped edges collimating skew light rays. 65.The backlight of claim 62, wherein each said curved facet and each saidsecond curved facet are arranged to preferentially direct a light fluxsubstantially normal to said top surface.
 66. The backlight of claim 65,wherein light flux enters said waveguide collimator from said lightinput end and said second light input end.
 67. A backlight comprising:acollimating waveguide having a light input end, a top surface, a bottomsurface, and opposing sides, said bottom surface converging toward saidtop surface in a direction along said backlight away from said lightinput end, said bottom surface comprising a plurality of curved facetshaving a density distributed along said bottom surface in a directionalong said backlight away from said light input end and extending atleast part way between said opposing sides, each said curved facethaving a curved facet bottom surface, each said curved facet bottomsurface being curved substantially in accordance with the equation:##EQU33## where β is the angle of a highest inclination incident ray andw and G are dimensions of said curved facet; and said plurality ofcurved facets causing light entering said light input end and reflectingfrom said plurality of curved facets to reflect from each said curvedfacet bottom surface symmetrically with respect to an axis normal tosaid top surface.